A243931 Number of isomorphism classes of 2-reductive involutory abelian/medial quandles.

1, 1, 2, 4, 10, 31, 120, 594, 4013, 35092, 428080, 6851545, 153025576, 4535778875, 187380634539, 10385121165057, 801710433900516

Offset: 1

Author

David Stanovsky, Oct 01 2014

Keywords

• nonn
• hard

Comments

Both names "abelian" and "medial" refer to the identity (xy)(uv)=(xu)(yv). A quandle is called 2-reductive if all orbits are projection quandles. A (left) quandle is involutory (aka symmetric, kei) if all (left) translations have order at most 2, i.e., x(xy)=y is satisfied.

Links

• Table of n, a(n) for n = 1..17
• P. Jedlička, A. Pilitowska, D. Stanovský, A. Zamojska-Dzienio, The structure of medial quandles, arXiv:1409.8396 [math.GR], 2014.
• David Stanovský, Calculating with quandles GAP code to calculate the numbers.

Crossrefs

Cf. A242044, A242275.